# Target Test Prep EA Quant Challenge Problem 3

### Challenge Question

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Last Sunday, the Stewart Vineyard ran a price promotion in which it sold red wine for r dollars per case and white wine for w dollars per case. What was the ratio of the revenue from red wine to the revenue from white wine?

1) Last Sunday, the Stewart Vineyard sold each case of red wine for 3 times as much as each case of white wine.

2) Last Sunday, the Stewart Vineyard sold 2 times as many cases of white wine as it sold of red wine.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Solution:

Question Stem Analysis:

If we let x = the number of cases of red wine sold, the revenue from red wine can be expressed as rx. Similarly, if we let y = the number of cases of white wine sold, the revenue from white wine can be expressed as wy. Thus, the ratio we're looking for is

revenue from red winerevenue from white wine=rxwy

Remember that we'll need to produce a constant ratio in order to produce a meaningful ratio.

Statement One Alone:

Last Sunday, the Stewart Vineyard sold each case of red wine for 3 times as much as each case of white wine.

This means that r = 3w, which we can substitute for r in our ratio:

revenue from red winerevenue from white wine=3wxwy=3xy

This is not sufficient because there are still two different variables in the fraction. Different values of x and y would change the value of the fraction. Statement one alone is not sufficient.

Eliminate answer choices A and D.

Statement Two Alone:

Last Sunday, the Stewart Vineyard sold 2 times as many cases of white wine as it sold of red wine.

This means that y = 2x, which we can substitute for y in our ratio:

revenue from red winerevenue from white wine=rxw2x=r2w

This ratio is not sufficient because there are two different variables in the fraction. Different values of r and w would change the value of the fraction. Statement two alone is not sufficient.